4.4/

Composite Rules

1. What?
   
2. Why?
   
3. Notice:

Composite Simpson’s rule

1. Composite Simpson’s rule:
   
2. Error in Comoposite Simpson’s Rule:
   

   Error:

3. Theorem [Rule and Error]:
   
4. Algorithm:
   

Composite Newton-Cotes Rules

1. Composite Trapezoidal rule:
2. Composite Midpoint rule:

Round-Off Error Stability

1. Stability Property:
   
2. Proof: